Estimating Rainfall Erosivity from Daily Precipitation Using Generalized Additive Models †

Proceedings Estimating Rainfall Erosivity from Daily Precipitation Using Generalized Additive Models † Konstantinos Vantas *, Epaminondas Sidiropoulos and Chris Evangelides Department of Rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece; [email protected] (E.S.); [email protected] (C.E.) * Correspondence: [email protected]; Tel.: +30-24670-24804 † Presented at the 4th EWaS International Conference: Valuing the Water, Carbon, Ecological Footprints of Human Activities, Online, 24–27 June 2020. Published: 13 August 2020 Abstract: One of the most important natural processes responsible for soil loss is rainfall-induced erosion. The calculation of rainfall erosivity, as defined in the Universal Soil Loss Equation, requires the availability of rainfall data, either continuous breakpoint, or pluviograph, with sampling intervals on the order of minutes. Due to the limited temporal coverage and spatial scarcity of such data, worldwide, alternative equations have been developed that utilize coarser rainfall records, in an effort to estimate erosivity equivalently to that calculated using pluviograph data. This paper presents the application of generalized additive models (GAMs) to estimate erosivity utilizing daily rainfall records. As a case study, pluviograph data with a time step of 30 min from the Water District of Thrace in Greece were used. By applying GAMs, it became possible to model the nonlinear relation between daily rainfall, seasonal periodicity, and rainfall erosivity more effectively, in terms of accuracy, than the application of two well-known nonlinear empirical equations, both on a daily and an annual basis. Keywords: rainfall erosivity; USLE; GAM; nonlinear regression; rainfall data; Greece 1. Introduction Rainfall erosivity concerns the ability of rainfall to cause erosion on the surface of the earth [1]. Unsustainable land management, growing human pressure on ecosystems, and possible higher erosion rates due to climate change [2] can lead to soil degradation and decreasing agricultural productivity, setting the ecologic balance in danger, and even reducing the efficiency of adaptation measures [3]. Accelerated soil losses and the menace of desertification, which many countries face [4], pose a danger to the achievement of the Sustainable Development Goals of the United Nations to end poverty [5], because these goals depend on a healthy environment and sustainable agricultural production. Regarding the calculation of soil erosion rates, it is a necessity to compute rainfall erosivity and simulate the effects of land use and the appliance of different land practices [6]. Due to the difficulty in modeling the distribution, size, and terminal velocity of raindrops in relation to the detachment of soil particles, more tractable rainfall indices have been utilized for the calculation of erosivity [7]. Therefore, in the Universal Soil Loss Equation (USLE) [8], the rainfall erosivity factor R was introduced as the product of the rainfall kinetic energy of a storm, classified as erosive by certain criteria, and its maximum 30 min intensity. USLE with its computerized revisions RUSLE [9] and RUSLE2 [10] are the most widely applied soil erosion prediction models globally [11]. A serious issue in the application of USLE is the computation of R, which requires pluviograph records with a length of at least twenty years, so that wet or dry rainfall periods will be incorporated, eliminating any bias [7]. In order to cope with the difficulties that arise due to the absence of adequate Environ. Sci. Proc. 2020, 2, 21; doi:10.3390/environsciproc2020002021 www.mdpi.com/journal/environsciproc Environ. Sci. Proc. 2020, 2, 21 2 of 8 pluviograph data, in terms of spatial and temporal coverage, many models have been developed. These models use empirical equations based on various coarser records of rainfall depths (daily, monthly, annual), under specific spatial parameters and climatological data, in order to estimate R. A comprehensive list of such methods can be found in Vantas et al. [12]. Additionally, these models can be used in conjunction with climate models in order to estimate projected changes in R [3]. The use of more efficient techniques, such as machine or statistical learning algorithms, to estimate erosivity is exiguous in the pertinent literature. Recently, Vantas et al. utilized quantile regression forests to estimate current and future values of R [3], and the same authors applied spatiotemporal clustering to define regions in Greece with similar erosivity density patterns [13]. Vantas et al. [12] compared the results from deep neural networks to empirical equations on the estimation of R, and Vantas and Sidiropoulos [14] evaluated the use of Bayesian neural networks on the estimation of weekly erosivity values. A generalized additive model (GAM) is a statistical learning algorithm [15], in the area of supervised learning, that can be used in classification and regression problems. This algorithm is an extension of generalized linear models (GLMs) that automatically fits a set of smoothing functions for each one of the input variables and adds all of these contributions, in order to estimate the output response [16]. In contrast to the use of ordinary linear regression or GLMs, GAMs provide more accurate results if nonlinear relationships exist [15]. In addition, GAMs are easier to interpret in comparison to other machine learning methods, such as random forests or neural networks, etc. [17]. Additionally, GAMs offer the ability to evaluate the results for each one of the terms of the model, to report the approximate significance of smooth terms and to produce confidence intervals of the output response [18]. Uses of GAM in hydrology are relatively scarce and can be found in regional low-flow frequency analysis [19], modeling extreme droughts [20], and empirical streamflow simulation [21]. This study aims to introduce and evaluate the use of GAMs for the estimation of erosivity using daily rainfall records. As a case study, pluviograph data of twelve stations from the Water District of Thrace in Greece were used. Firstly, erosive storms were extracted and their erosivity was calculated using the procedure described in RUSLE2. Subsequently, the calculated erosivity values and precipitation timeseries were aggregated on a daily basis. Afterward, a GAM model and two empirical exponential equations were fitted utilizing the aggregated values. Finally, the performance of the fitted models on estimating daily and annual erosivity was validated, in relation to the directly calculated values, using an independent test set. This type of analysis is a novel approach and it has not been presented, until now, in the international literature. 2. Materials and Methods 2.1. Data Acquisition and Processing The study region, located to the north-east of Greece (Figure 1), extends to an area of 11,243 km2 that covers the Water District of Thrace. It is delimited by the boundaries of Greece with Bulgaria and Turkey on the north and east, respectively, by the Thracian Sea on the south, and by the watershed of Nestos River on the west. This area was identified: (a) To have common rainfall erosivity spatiotemporal patterns [3]; (b) to form a region with a distinct monthly temporal distribution of erosivity density [13], a parameter strongly related to seasonal rainfall intensity [10]; and (c) to have similar intra-storm temporal distribution intensity patterns of heavy and, consequently, erosive precipitation [22]. Pluviograph data for 12 meteorological stations were taken from the Greek National Bank of Hydrological and Meteorological Information (NBHM) [23]. The time series comprised a total of 372 years of pluviograph records with a time step of 30 min for the time period from 1965 to 1996 (Table 1). The time series rainfall records were checked for consistency and cleared from errors. Environ. Sci. Proc. 2020, 2, 21 3 of 8 Table 1. Meteorological station locations and record data durations. Name Latitude (°) Longitude (°) Elevation (m) Duration (y) 1 TOXOTES 41.09 24.79 75 27 2 M. DEREIO 41.32 26.10 116 22 3 FERRES 40.90 26.17 43 31 4 PARANESTI 41.27 24.50 122 34 5 GRATINI 41.14 25.53 120 27 6 KECHROS 41.23 25.86 700 24 7 M. KSIDIA 41.13 25.64 70 27 8 THERMES 41.35 25.01 440 26 9 GERAKAS 41.20 24.83 308 24 10 ORAIO 41.27 24.83 656 26 11 SEMELH 41.09 24.84 65 23 12 CHRYSOUPOLI 40.99 24.69 15 14 Figure 1. Station locations used in the analysis in the Greek Water District of Thrace. 2.2. Rainfall Erosivity Calculations The erosivity of a single erosive rainfall event, (MJ·mm/ha/h), was computed using the pluviograph records [1]: = ⋅⋅30 (1) where is the kinetic energy per unit of rainfall (MJ/ha/mm), the rainfall depth (mm) for the time interval of the hyetograph, which has been divided into = 1,2, … , time sub-intervals, and 30 is the maximum rainfall intensity for a 30 min duration during that rainfall. The quantity was calculated for each time sub-interval, , applying the kinetic energy equation used in RUSLE2 [10]: 0.82 = 0.29(1−0.72 ) (2) where is the rainfall intensity (mm/h). Environ. Sci. Proc. 2020, 2, 21 4 of 8 An individual rainfall event was extracted from the continuous pluviograph data, if its cumulative depth for a duration of 6 h at a certain location was less than 1.27 mm. A rainfall event was considered to be erosive if it had a cumulative rainfall depth greater than 12.7 mm. Given that the use of coarser fixed time intervals as 30 min to a finer one can lead to an underestimation of the value of erosivity, the appropriate monthly conversion factors, previously computed for Greece [3], were applied. The daily erosivity (MJ·mm/ha/h/d) was either set equal to the sum of all daily events or when a storm was crossed temporally by two or more consecutive days; it was assigned to the first calendar day: = () (3) where =1,..., are the erosive events that initiate during calendar day d.

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